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Latent Variables Analysis in Structural Models: A New Decomposition of the Kalman Smoother

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Abstract

This paper advocates chaining the decomposition of shocks into contributions from forecast errors to the shock decomposition of the latent vector to better understand model inference about latent variables. Such a double decomposition allows us to gauge the inuence of data on latent variables, like the data decomposition. However, by taking into account the transmission mechanisms of each type of shock, we can highlight the economic structure underlying the relationship between the data and the latent variables. We demonstrate the usefulness of this approach by detailing the role of observable variables in estimating the output gap in two models.

Suggested Citation

  • Hess T. Chung & Cristina Fuentes-Albero & Matthias Paustian & Damjan Pfajfar, 2020. "Latent Variables Analysis in Structural Models: A New Decomposition of the Kalman Smoother," Finance and Economics Discussion Series 2020-100, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2020-100
    DOI: 10.17016/FEDS.2020.100
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    1. Peter N. Ireland, 2011. "A New Keynesian Perspective on the Great Recession," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(1), pages 31-54, February.
    2. Marco Del Negro & Marc P. Giannoni & Frank Schorfheide, 2015. "Inflation in the Great Recession and New Keynesian Models," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 168-196, January.
    3. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    4. Robert Barsky & Alejandro Justiniano & Leonardo Melosi, 2014. "The Natural Rate of Interest and Its Usefulness for Monetary Policy," American Economic Review, American Economic Association, vol. 104(5), pages 37-43, May.
    5. Nicholas Sander, 2013. "Fresh perspectives on unobservable variables: Data decomposition of the Kalman smoother," Reserve Bank of New Zealand Analytical Notes series AN2013/09, Reserve Bank of New Zealand.
    6. Andrle, Michal, 2012. "Understanding DSGE Filters in Forecasting and Policy Analysis," Dynare Working Papers 16, CEPREMAP.
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    More about this item

    Keywords

    Kalman smoother; latent variables; Shock decomposition; Data decomposition; Double decomposition;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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